The desnsity of the atmosphere at sea level is 1.29 kg/m^3.. Assume that it does not change with altitude. Then how high would the atmosphere extend?

The atmospheric pressure at the sea level is

$P_0=1.01\times {10}^{5}N/m^2$

now the height of atmosphere is h

$P_0={\rho }_{air}gh$

$\Rightarrow h=\frac{P_0}{{\rho }_{air}g}$

substituting the values,

$h=\frac{1.01\times {10}^5}{1.29\times 9.8}=7989 m\simeq 8 km$